In many applications, electronic signals contain phase information, which when processed provide useful information, such as images, distances, velocities, topography maps, and the like. For example, a Synthetic Aperture Radar (SAR) system uses several radar scans from a source, such as an airplane or a satellite, to construct a topographic map of large areas of land. Similarly, received radar scan signals may be processed to determine the distance of a target from a receiving system.
Other applications that use phase information include magnetic resonance imaging (MRI), interferometry, X Ray crystallography, and optical Doppler tomography where the phase difference in the two received signals is used to measure the velocity of blood within a tissue.
Phase wrapping refers to phase values of greater than 2π or less than zero. When a measuring system measures phase values between 0 degrees and 360 degrees (2π radians) and angles over 2π are registered as the difference between actual angle and 360 degrees, the phase measurement results in phase jumps, when there are phase angles greater than 2π. Since the measuring system only measures angles between zero and 2π, a resultant phase angle between zero and 2π may be “wrapped around” as an angle greater than 2π. Determining whether a measured angle is within or outside the range of zero to 2π and correcting out-of-range values is referred to as phase unwrapping. It is desirable to perform phase unwrapping, because mathematical manipulations of the phase information (phase map) require continuity in the phase of measured signal, such as to correct field in homogeneities in MR applications or to generate accurate images using radar distance measurements.
Conventional phase unwrapping techniques consist of detecting node (pixel) locations of the phase discontinuities, finding an ordering among node locations for unwrapping the phase, and adding offsets of multiples of 2π to them. Phase unwrapping is computationally intensive and therefore is often performed by computationally powerful, off-line systems under user guidance.
Accordingly, there is a need for a fast, computationally efficient phase unwrapping methodology for correcting phase jumps for phase information-based applications.